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Algebraic Geometry I Semester
WiSe 2019 / 20
Lecturer
Prof. Dr. Klaus Kuennemann
Type of course (Veranstaltungsart)
Vorlesung
Contents
This course offers a first introduction to algebraic geometry. We study algebraic varieties and more
generally algebraic schemes. These are geometric objects which are defined locally as solutions of
systems of polynomial equations. We develop the basic theory of algebraic varieties and schemes,
i.e. affine and projective varieties, Zariski topology, Krull dimension, sheaves, schemes, coherent
modules, divisors, line bundles, differentials etc. As a prerequisite basic knowledge of commutative
algebra and some algebra is assumed. The course is fundamental for all students who plan to
specialize in the direction of Arithmetic Geometry (MArGeo) and will continue in the summer term
2020 as 'Algebraic Geometry II'.
Recommended previous knowledge
Commutative Algebra and some Algebra
Time/Date
Mo, Do 10h15 - 12h00
Location
M101 (Mo), M104 (Do)
Registration- Preliminary registration for the organisation of exercise classes: at the end of the previous
semester via EXA or LSF (see announcement by the department) - Registration for the exercise classes: During the first week of the teaching period. More
information will be given in the lecture. - Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)- Successful participation in the exercise classes: Active participation and the presentation of
solutions to exercises at the blackboard: Each participant has to present at least two
solutions, at least one from the exercise sheets 1-6 and at least one from the exercise sheets
7-12. Furthermore written solutions to the exercises have to be submitted (at least 25%
successful solutions from sheet 1-6 and at least 25% successful solutions from sheet 7-12).
Examination (Prüfungsleistungen)- Oral exam: Duration: 30 minutes, Date: by individual appointment, re-exam: Date: by individual
appointment - Combined exam in agreement with the lecturer in combination with, e.g.: Algebraic geometry II,
oral exam: Duration: 30 minutes, Date: by individual appointment
Regelungen bei Studienbeginn vor WS 2015 / 16- Benotet:
- O. g. Studienleistung und o. g. Prüfungsleistung; die Note ergibt sich aus der Prüfungsleistung
- Unbenotet:
- O. g. Studienleistung und Bestehen der o. g. Prüfungsleistung
Modules
BV, MV, MArGeo, LA-GyAlg
ECTS
9 ECTS
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